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An interview with Themistocles M. Rassias. (English) Zbl 1175.01074

Summary: While the authors were visiting Athens in 2006 and 2005, respectively, they interviewed Professor Themistocles M. Rassias concerning his contributions to Mathematics. This article presents those interviews.

MSC:

01A70 Biographies, obituaries, personalia, bibliographies
39-03 History of difference and functional equations

Biographic References:

Rassias, Themistocles M.
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References:

[1] M. Amyari and M.S. Moslehian, Approxiamtely ternary semigroup homomorphisms , Lett. Math. Phys. 77 (2006), 1-9. · Zbl 1112.39021 · doi:10.1007/s11005-005-0042-6
[2] T. Aoki, On the stability of the linear transformation in Banach spaces , J. Math. Soc. Japan 2 (1950) 64-66. · Zbl 0040.35501 · doi:10.2969/jmsj/00210064
[3] C.Baak, D.-H. Boo and Th.M. Rassias, Generalized additive mapping in Banach modules and isomorphisms between \(C^*\)-algebras , J. Math. Anal. Appl. 314 (2006), 150-161. · Zbl 1090.39015 · doi:10.1016/j.jmaa.2005.03.099
[4] B. Belaid, E. Elhoucien and Th.M. Rassias, On the generalized Hyers-Ulam stability of the quadratic functional equation with a general involution , Nonlinear Funct. Anal. Appl. (to appear). · Zbl 1138.39024
[5] B. Belaid, E. Elhoucien and Th.M. Rassias, On the Hyers-Ulam stability of approximately Pexider mappings , Math. Ineq. Appl. (to appear). · Zbl 1163.39016
[6] M. Craioveanu, M. Puta and Th.M. Rassias, Old and New Aspects in Spectral Geometry , Kluwer Academic Publishers, Dordrecht, Boston, London, 2001. · Zbl 0987.58013
[7] S. Czerwik, Functional Equations and Inequalities in Several Variables , World Scientific, New Jersey, London, Singapore, Hong Kong, 2002. · Zbl 1011.39019
[8] S.S. Dragomir and Th.M. Rassias, A mapping associated with Jensen’s inequality and applications , Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 44 (92) (2001), no. 2, 155-164. · Zbl 1049.26013
[9] V. Faĭ ziev, Th.M. Rassias and P.K. Sahoo, The space of \((\psi,\gamma)\)-additive mappings on semigroups Trans. Amer. Math. Soc. 354 (2002), no. 11, 4455-4472. JSTOR: · Zbl 1043.20035 · doi:10.1090/S0002-9947-02-03036-2
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[11] P. Găvruţa, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings , J. Math. Anal. Appl. 184 (1994), 431-436. · Zbl 0818.46043 · doi:10.1006/jmaa.1994.1211
[12] H. Haruki and Th.M. Rassias, A new characterization of Möbius transformations by use of Apollonius hexagons , Proc. Amer. Math. Soc. 128 (2000), 2105-2109. JSTOR: · Zbl 0943.30007 · doi:10.1090/S0002-9939-00-05246-1
[13] D.H. Hyers, On the stability of the linear functional equation , Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. · Zbl 0061.26403 · doi:10.1073/pnas.27.4.222
[14] D.H. Hyers, G. Isac and Th.M. Rassias, Topics in Nonlinear Analysis and Applications , World Scientific Publishing Co., Singapore, New Jersey, London, 1997. · Zbl 0878.47040
[15] D.H. Hyers, G. Isac and Th.M. Rassias, Stability of Functional Equations in Several Variables , Birkhäuser, Basel, 1998. · Zbl 0907.39025
[16] D.H. Hyers, G. Isac and Th.M. Rassias, On the asymptoticity aspect of Hyers-Ulam stability of mappings , Proc. Amer. Math. Soc. 126 (1998), 425-430. JSTOR: · Zbl 0894.39012 · doi:10.1090/S0002-9939-98-04060-X
[17] D.H. Hyers and Th.M. Rassias, Approximate homomorphisms , Aequationes Math. 44 (1992), 125-153. · Zbl 0806.47056 · doi:10.1007/BF01830975
[18] G. Isac and Th.M. Rassias, Stability of \(\psi\)-additive mappings: Applications to nonlinear analysis , Internat. J. Math. Math. Sci. 19 (1996), 219-228. · Zbl 0843.47036 · doi:10.1155/S0161171296000324
[19] G. Isac and Th.M. Rassias, On the Hyers-Ulam stability of \(\psi\)-additive mappings , J. Approx. Theory 72 (1993), 131-137. · Zbl 0770.41018 · doi:10.1006/jath.1993.1010
[20] S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis , Hadronic Press, Palm Harbor, 2001. · Zbl 0980.39024
[21] S.-M. Jung and Th.M. Rassias, Ulam’s problem for approximate homomorphisms in connection with Bernoulli’s differential equation , Appl. Math. Comput. 187 (2007), 223-227. · Zbl 1118.39014 · doi:10.1016/j.amc.2006.08.120
[22] S.-M. Jung and Th.M. Rassias, Generalized Hyers-Ulam stability of Riccati differential equation , Math. Inequal. Appl. (to appear). · Zbl 1200.39010
[23] J.-R. Lee and D.Y. Shin, On the Cauchy-Rassias stability of the Trif functional equation in \(C^*\)-algebras , J. Math. Anal. Appl. 296 (2004), 351-363. · Zbl 1064.46039 · doi:10.1016/j.jmaa.2004.04.028
[24] B. Mielnik and Th.M. Rassias, On the Aleksandrov problem of conservative distances , Proc. Amer. Math. Soc. 116 (1992), 1115-1118. · Zbl 0769.51005 · doi:10.2307/2159497
[25] G.V. Milovanović, D.S. Mitrinović and Th.M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, Zeros , World Scientific Publishing Co., Inc., River Edge, NJ, 1994. · Zbl 0848.26001
[26] M.S. Moslehian, Ternary derivations, stability and physical aspects , Acta Appl. Math. (to appear). · Zbl 1135.39014 · doi:10.1007/s10440-007-9179-x
[27] M.S. Moslehian and Th.M. Rassias, Orthogonal stability of additive type equations , Aequationes Math., 73 (2007) 249-259. · Zbl 1122.39022 · doi:10.1007/s00010-006-2868-0
[28] M. S. Moslehian and Th. M. Rassias, Stability of functional equations in non-Arhimedian spaces , Appl. Anal. Disc. Math. 1 (2007), 325-334. · Zbl 1257.39019 · doi:10.2298/AADM0702325M
[29] M.S. Moslehian and Th.M. Rassias, Generalized Hyers-Ulam stability of mappings on normed Lie triple systems , Math. Inequal. Appl. (to appear). · Zbl 1144.39026
[30] M.A. Noor, K.I. Noor and Th.M. Rassias, Some aspects of variational inequalities J. Comput. Appl. Math. 47 (1993), 285-312. · Zbl 0788.65074 · doi:10.1016/0377-0427(93)90058-J
[31] M.A. Noor, K.I. Noor and Th.M. Rassias, Set-valued resolvent equations and mixed variational inequalities J. Math. Anal. Appl. 220 (1998), 741-759. · Zbl 1021.49002 · doi:10.1006/jmaa.1997.5893
[32] C.-G. Park, Generalized quadratic mappings in several variables , Nonlinear Anal. 57 (2004), 713-722. · Zbl 1058.39024 · doi:10.1016/j.na.2004.03.013
[33] C.-G. Park and Th.M. Rassias, Hyers-Ulam stability of a generalized Apollonius type quadratic mapping , J. Math. Anal. Appl. 322 (2006), 371-381. · Zbl 1101.39020 · doi:10.1016/j.jmaa.2005.09.027
[34] C.-G. Park and Th.M. Rassias, The \(N\)-isometric isomorphisms in linear \(n\)-normed \(C^*\)-algebras , Acta Math. Sinica (English Series), 22 (2006), 1863-1890. · Zbl 1125.39028 · doi:10.1007/s10114-005-0878-9
[35] C.-G. Park and Th.M. Rassias, Inequalities in additive \(N\)-isometries on linear \(N\)-normed Banach spaces, J. Inequal. Appl., 2007 (2007), Article ID 70597, pp.1-12. · Zbl 1132.39027 · doi:10.1155/2007/70597
[36] A. Prastaro and Th.M. Rassias, Ulam stability in geometry of PDE’s , Nonlinear Funct. Anal. Appl. 8 (2003), 259-278. · Zbl 1096.39028
[37] J. M. Rassias, On approximation of approximately linear mappings by linear mappings , J. Funct. Anal. 46 (1982), 126-130. · Zbl 0482.47033 · doi:10.1016/0022-1236(82)90048-9
[38] Th.M. Rassias, On the stability of the linear mapping in Banach spaces , Proc. Amer. Math. Soc. 72 (1978), 297-300. · Zbl 0398.47040 · doi:10.2307/2042795
[39] Th.M. Rassias, Problem 16 ; 2, Report of the 27th International Symp.on Functional Equations , Aequationes Math. 39 (1990), 292-293; 309.
[40] Th.M. Rassias, On the stability of functional equations in Banach spaces , J. Math. Anal. Appl. 251 (2000), 264-284. · Zbl 0964.39026 · doi:10.1006/jmaa.2000.7046
[41] Th.M. Rassias (ed.), Functional Equations, Inequalities and Applications , Kluwer Academic Publishers, Dordrecht, Boston and London, 2003. · Zbl 1047.39001
[42] Th.M. Rassias, Is a distance one preserving mapping between metric spaces always an isometry? Amer. Math. Monthly 90 (1983), 200. · Zbl 0512.54017 · doi:10.2307/2975550
[43] Th.M. Rassias, On the stability of mappings , Rendiconti del Seminario Matematico e Fisico di Milano 58 (1988), 91-99. · Zbl 0711.47002 · doi:10.1007/BF02925233
[44] Th.M. Rassias, On a modified Hyers-Ulam sequence , J. Math. Anal. Appl. 158 (1991), 106-113. · Zbl 0746.46038 · doi:10.1016/0022-247X(91)90270-A
[45] Th.M. Rassias, On the stability of the quadratic functional equation and its applications , Studia Univ.Babes-Bolyai Math. 43 (1998), 89-124. · Zbl 1009.39025
[46] Th.M. Rassias, On the stability of functional equations originated by a problem of Ulam , Mathematica. 44 (67)(1) (2002), 39-75. · Zbl 1084.39504
[47] Th.M. Rassias, The problem of S.M.Ulam for approximately multiplicative mappings , J. Math. Anal. Appl. 246 (2) (2000), 352-378. · Zbl 0958.46022 · doi:10.1006/jmaa.2000.6788
[48] Th.M. Rassias, On the stability of functional equations and a problem of Ulam , Acta Appl. Math. 62 (2000), 23-130. · Zbl 0981.39014 · doi:10.1023/A:1006499223572
[49] Th.M. Rassias, Stability of the generalized orthogonality functional equation , in: Inner Product Spaces and Applications, Addison Wesley Longman, Pitman Research Notes in Mathematics Series No. 376 (ed. Th.M. Rassias), 1997, pp. 219-240. · Zbl 0891.39024
[50] Th.M. Rassias, Stability and set-valued functions , in: Analysis and Topology (ed.Th.M. Rassias), World Scientific Publishing Co., 1998, pp. 585-614. · Zbl 0939.39017
[51] Th.M. Rassias, Properties of isometric mappings , J. Math. Anal. Appl. 235 (1999),108-121. · Zbl 0936.46009 · doi:10.1006/jmaa.1999.6363
[52] Th.M. Rassias, Isometries and approximate isometries , Internat J. Math. Math. Sci. 25 (2) (2001), 73-91. · Zbl 0990.46004 · doi:10.1155/S0161171201004392
[53] Th.M. Rassias, On the stability of minimum points , Mathematica 45(68)(1) (2003),93-104. · Zbl 1084.49026
[54] Th.M. Rassias, On the A.D. Aleksandrov problem of conservative distances and the Mazur-Ulam theorem , Nonlinear Anal., 47 (4) (2001), 2597-2608. · Zbl 1042.51500 · doi:10.1016/S0362-546X(01)00381-9
[55] Th.M. Rassias and P. Šemrl, On the behaviour of mappings which do not satisfy Hyers-Ulam stability , Proc. Amer. Math. Soc. 114 (1992), 989-993. JSTOR: · Zbl 0761.47004 · doi:10.2307/2159617
[56] Th.M. Rassias and P. Šemrl, On the Mazur-Ulam theorem and the Aleksandrov problem for unit distance preserving mappings , Proc. Amer. Math. Soc. 118 (1993), 919-925. · Zbl 0780.51010 · doi:10.2307/2160142
[57] Th.M. Rassias and P. Šemrl, On the Hyers-Ulam stability of linear mappings , J. Math. Anal. Appl. 173 (1993), 325-338. · Zbl 0789.46037 · doi:10.1006/jmaa.1993.1070
[58] Th.M. Rassias and J. Simsa, Finite Sums Decompositions in Mathematical Analysis , John Wiley & Sons, Wiley-Interscience Series in Pure and Applied Mathematics, 1995. · Zbl 0859.26005
[59] Th.M. Rassias and J. Tabor, What is left of Hyers-Ulam stability? , J. Natur. Geom. 1 (1992), 65-69. · Zbl 0757.47032
[60] Th.M. Rassias and S. Xiang, On Mazur-Ulam theorem and mappings which preserve distances , Nonlinear Funct. Anal. Appl. 5 (2000), 61-66. · Zbl 0981.46008
[61] L. Tan and S. Xiang, On the Aleksandrov-Rassias problem and the Hyers-Ulam-Rassias stability problem , Banach J. Math. Anal. 1 (2007), 11-22. · Zbl 1130.39027
[62] S.M. Ulam, Problems in Modern Mathematics , Chapter VI, Science Editions, Wiley, New York, 1964. · Zbl 0137.24201
[63] S. Xiang, On the Aleksandrov-Rassias problem for isometric mappings Functional equations, inequalities and applications, 191-221, Kluwer Acad. Publ., Dordrecht, 2003. · Zbl 1075.46010
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